Numerical Expression

Introduction to Numerical Expression

In this topic, we will learn the definition of a numerical expression, what is the meaning of numerical and learn how to write a number in numerical form. We will discuss here the simplification of numerical expressions. Students will be provided with plenty of examples to clearly illustrate this important mathematical concept. When we look at a problem with numbers, we are most likely looking at a numerical expression. In this article, we will explain how to simplify numerical expressions with the help of various numerical expression examples.


What is the Meaning of Numerical?

Numerical Definition-The term numerical means involving numbers.


The term numerical expression consists of two words, numerical meaning numbers and expression meaning phrase. Thus, it is a phrase involving numbers.  A numerical expression in mathematics is a combination of numbers integers combined using mathematical operators such as addition, subtraction, multiplication, or division.


There are different forms in which the number can be expressed,, such as word form and numerical form.


A numerical expression is a mathematical statement that involves only numbers along with one or more operation symbols. Examples of operation symbols are addition, subtraction, multiplication and division. It can also be expressed in the radical symbol (the square root symbol) or the absolute value symbol.


Numerical Expression Example

A numerical expression is formed by the combination of numbers, including various mathematical operators. There is no limit to the number of operators that a numerical expression may contain. Some numerical expressions use only one operator between two numbers, whereas some may contain more than one. 


The only requirements for a numerical expression are that it only contains numbers and operation symbols. Some numerical expressions have only one operation symbol. Others have two or more. 


Here are Some Examples of Numerical Expressions

4 + 5

134 - 75

56 * 4 + 6

60/5*7-2+1


Examples of Non-Numerical Expressions:

As we know, numerical expressions can only contain numbers; expressions containing variables (such as x or y) cannot be considered numerical expressions. They are actually called algebraic expressions instead. Given below are two examples of algebraic expressions:


2x + 5


250 - y


How to Write Numerical Expression?

Any mathematical word problem is solved by first converting it into a numerical expression. 


Below we have provided one example to understand it. 


Question: Nancy has 10 chocolate bars. She gives 3 chocolates to her sister, 1 to her friend and eats 2. Later she visits her grandmother, and she (grandmother) offers Nancy 12 more chocolate bars. How many chocolate bars does Nancy have now? 


Solution: Here first look at the numbers involved in the above problem. Nancy has 10 chocolate bars. She gives away 4 (3 to her sister and 1 to her friend), eats 2 and then again gets 12 chocolate more from her grandmother. So, it can be represented in numerical expression as  10 - 3 - 1 - 2 + 12     

    = 7 - 1 - 2 + 12     

    = 6 - 2 + 12     

    = 4 + 12     

    = 16


Hence, Nancy has now 16 chocolate bars.


Did you know?

Power can also be expressed as a numerical expression. It has two parts: an exponent and a base.


(Image will be Uploaded Soon)


2⁴ can be written as 2.2.2.2


An expression can also be a combination of variables and constants that are combined using mathematical operations. Such expression is known as an algebraic expression.


Simplification of Numerical Expressions

To simplify a numerical expression that has two or more operations, we perform the BODMAS rule. In this rule, we have to solve operations like Brackets, order of powers or roots, Division first, followed by Multiplication, Addition and then Subtraction. A standard result called BODMAS is followed for simplification of these operations.

The word BODMAS stands for:

B → Brackets

O → Order of powers or roots

D → Division

M → Multiplication

A → Addition

S → Subtraction


If the brackets are present in the problem, first, we have to simplify the brackets. There are four kinds of brackets.

  1.  ( ) → This symbol is simple brackets or round brackets or parenthesis.

  2.  { } → Braces or Curly brackets.

  3. [ ]→ Square brackets.

  4.  ______ → This symbol is a line called bar or vinculum. It is used when two or more types of brackets are involved in the problem. Brackets are removed in this order ‘_________’, ( ), { }, [ ]


Simplify the Following Numerical Expressions

(i) Solve

10+7−(8÷2) × 3

First, we will solve the round bracket

=10+7−4 × 3 

=17-12

=5

Hence the final value is 5


(ii) Find the Value of 15 +20−8+(6÷2)

First, remove the round bracket

= 15 +20−8+3

=35-8+3

=38-8

=30

Hence the final value is 30


(iii) Evaluate the Numerical Expression 10² - 10 + 100

Fist evaluate the square value

= 10 x 10 - 10 + 100

=100-10+100

=90+100

=190

Hence the final value is 190.

FAQs on Numerical Expression

1. What is a Numerical Expression?

There are mainly four fundamental operations while simplifying any numerical expression. They are addition, subtraction, multiplication and division, which includes whole numbers, fractional numbers and decimals also. While solving any numerical expression, the general process is to perform one operation at a time. But to simplify numerical expression with two or more operations, a standard procedure BODMAS is used to simplify these operations.

2. How are Real-world Problems in Which We Use the Numerical Expression?

We know that numerical expressions are expressions that contain numbers and operations, namely addition, subtraction, multiplication and division. In this way, there are numerous real-life situations that are easily solved with the help of numerical expressions, such as when we need to find how much discount is applied to a product, to find the area of a rectangular park, to find the number of ingredients required to bake a cake and many more.

3. What are the Steps Needed to Follow While Solving Numerical Expression?

Following are the steps to solve numerical expression:

Step 1: First, simplify the operations inside grouping symbols.

Step 2: Simplify the powers.

Step 3: Solve multiplication and division followed by a left to right.

Step 4: Finally, solve addition and subtraction from left to right.

4. What is a Numerical Expression Example?

In General, Numerical Expression is a combination of two words that is Numeric and Expression means numbers and phrases. So we can say that Numerical Expression is a phrase that also involves numbers. In mathematics, numerical expression is said to be a combination of different numbers integers combined with the help of mathematical operators such as addition, subtraction, multiplication, or division.


Mentioned below are some common examples of Numerical Expression:


5 + 10


150 - 25


20 × 2 + 5 


40 ÷ 10 × 2 - 8 + 1 


75 + 6 - 8 

Comment